The soprano Hildegard Behrens, who has died of a ruptured aortic aneurism aged 72, was an individual, unforgettable Wagner singer, a great actor and, for many, the definitive interpreter of Richard Strauss's Salome and Elektra.

Born in Varel, not far from Hamburg in Germany, Behrens was the youngest child in a large family persuaded, like all her siblings, to take up an instrument by their music-loving doctor father (in her case the violin in addition to the piano). Graduating from her law studies at Freiburg University – a discipline which later came in useful when she negotiated her own contracts – Behrens took up singing there under Inés Leuwen. She started out belatedly in the lyric soprano repertoire, making her debut in 1971 as the Countess in Mozart's Marriage of Figaro and graduating via Fiordiligi and Weber's Agathe to the lighter Wagnerian roles.

In 1977, alerted that there was a remarkable young singing actor who might meet his Straussian standards, Herbert von Karajan travelled to Dusseldorf to see Behrens in the lacerating role of Marie in Berg's Wozzeck. He signed her up to sing Salome at the Salzburg festival, and the rest is history. From that, and the subsequent EMI recording, it was clear that from a tonal point of view, at last Strauss's stipulation for the illusion of a "16-year-old princess with the voice of an Isolde" had been realised.

In 1978 Covent Garden audiences, who had already been able to witness the birth of a legend two years earlier, when Behrens sang Leonore in Beethoven's Fidelio, saw that Salome for themselves – though this time there was no body double for the Dance of the Seven Veils, as Karajan had insisted on in Salzburg; Behrens performed the dance herself, as she was always subsequently to do.

Despite a vocal indisposition which Behrens was determined to ignore, her Royal Opera Salome was an electrifying interpretation. She started out with the silvery lightness of a gracious adolescent, developing with terrifying intensity into her crazed obsession for the head of John the Baptist. The great final scene married luminous fulfilment with disturbing mania. Never in recent memory has any soprano fulfilled so many of the role's impossible demands so vividly.

Soon, Behrens progressed to the even more taxing demands of the revenge-crazed Elektra in Strauss's violent next opera, a role she made her own in a blazing concert performance at the Royal Festival Hall and in a subsequent run at the Royal Opera. Leonard Bernstein chose her as his Isolde in a recording of Wagner's great love story, which taxed her breath control to extremes with its slow tempi. She gave birth to a daughter during the run of performances.

She soon stepped into the heroic shoes of Kirsten Flagstad and Birgit Nilsson as Wagner's Brünnhilde, very much on her own terms; with a lyric voice of dramatic potential rather than a true hochdramatisch capacity, the peculiar luminosity of Behrens's instrument always carried to the back even of a vast theatre like New York's Metropolitan Opera. Insistent use on a strong chest voice weakened the range and, in later years, the voice suffered from wear and tear, but her sheer commitment invariably carried all before it.

The traditional Met and under-energised Bayreuth productions of Wagner's Ring demanded less of Behrens's true dramatic potential than many would have liked to see, but she came into her own for Nikolaus Lehnhoff in Munich and in an unforgettable concert series conducted by Bernard Haitink at the Birmingham Symphony Hall and the Royal Albert Hall, London, as late as 1998. Brünnhilde nearly did for her, too, but not in the way it does for most sopranos: in 1990 the scenery fell on her during her immolation scene at the Met and, though she walked off stage, she was immediately hospitalised and subsequently took up a special vegetarian diet intended to help with the ensuing spinal problems.

In later years she progressed to roles which made demands of a different sort: the tormented Kundry in Wagner's Parsifal, the Kostelnicka in Janácˇek's Jenufa and Emilia Marty, the 337-year-old heroine of Janácˇek's The Makropoulos Case. Her legacy in recordings follows her path from the sweet heroine of Weber's Der Freischütz for Rafael Kubelik through to the unique Salome and the soldier's mistress in Claudio Abbado's sensuous interpretation of Wozzeck – a role also filmed – which gives a far stronger impression of her realistic acting than Brünnhilde in the conventional Otto Schenk Ring at the Met.

Behrens collapsed while giving master-classes and planning a recital at the Kusatsa summer music festival, to which she was a frequent visitor. She is survived by a son and a daughter.

•Hildegard Behrens, soprano, born 9 February 1937; died 18 August 2009